The battery charger for an mp3 player contains a step-down transformer with a turns ratio of 1: 38, so that the voltage of 120 v available at a wall socket can be used to charge the battery pack or operate the player. what voltage does the secondary coil of the transformer provide?

Transformer contains two coils: primary and secondary. They allow change of voltage to lower or higher value. In first case we have step-down and in second case we have step-up transformer.
Formula used for transformer is:

Where:N1 = number of turns on primary coilN2 = number of turns on secondary coilV1 = voltage on primary coilV2 = voltage on secondary coil
In a step-down transformer primary coil has more turns than secondary coil. So the ratio 1:38 means that for each turn on secondary coil we have 38 turns on primary coil.
We can solve the equation for V2:

Secondary coil provides voltage of 3.16V.